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Influence of alloy inhomogeneities on the determination by Raman scattering of composition and strain in Si1– x Ge x /Si(001) layers
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Image of FIG. 1.
FIG. 1.

(a) Representative Raman spectra of the Si1 x Ge x as-grown samples with and the Raman intensity plotted in logarithmic scale. (b) Representative spectra of the as-grown sample with and for different annealing temperatures. Peak assignment to the alloy optical Raman modes is indicated.

Image of FIG. 2.
FIG. 2.

Out-of-plane lattice parameter ( ) of the SiGe alloy layers determined by XRD measurements as a function of the annealing temperature for samples A to E. The vertical line corresponds to the as-grown samples. Error bars of the data points are around  Å.

Image of FIG. 3.
FIG. 3.

Computed values for using Eqs. (4) and (5) for each vibrational mode and annealing temperature. The dashed and solid curves represent the values of from Refs. 24 and 28 , respectively. Error bars of the data points (not shown since they are smaller than the symbol size) are around  cm 1.

Image of FIG. 4.
FIG. 4.

Three dimensional plots showing the solutions of Eqs. (8) and (9) for the Ge-Ge (violet) and Si-Si (orange) modes, respectively. In panel (a), we show the two surfaces for the as-grown sample E. The same surfaces are shown in (b) for sample E after all the annealing sequences. The physically reasonable solutions are given by the intersection of the two dimensional surfaces as marked with a white line.

Image of FIG. 5.
FIG. 5.

Solutions of Eqs. (8) and (9) for all the as-grown samples (solid lines) and annealed ones (circled lines) represented in the plane. The dotted black lines connect points with constant values of compositional inhomogeneity degree , representing real solutions, whereas the grey dotted lines are a guide to the eye, representing estimated solutions.


Generic image for table
Table I.

Si1− x Ge x alloy-layer thickness (d) of the different samples determined by spectral ellipsometry. Ge content for the as-grown layers obtained from XRD measurements (xxrd ) and using the model discussed in Sec. IV B (xmodel ). Numbers in parentheses represent error bars.

Generic image for table
Table II.

Composition dependence of the strain shift coefficients for the Ge-Ge, Si-Ge, and Si-Si modes extracted from Ref. 24 . Lattice constants and elastic constants extracted from Refs. 32 and 33 , respectively. The polynomial parameters for the unstrained frequencies were obtained by a combined fit to the data of Refs. 28 and 34 .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Influence of alloy inhomogeneities on the determination by Raman scattering of composition and strain in Si1–xGex/Si(001) layers